Noise driven dynamic phase transition in a a one dimensional Ising-like model

The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $β$ such that $β=0$ corresponds to the Ising model and $β\to \infty$ to the original model I. The equilibrium behaviour for any value of $β$ is identical: a homogeneous state. We argue, from the behaviour of the dynamical exponent $z$,that for any $β\neq 0$, the system belongs to the dynamical class of model I indicating a dynamic phase transition at $β= 0$. On the other hand, the persistence probabilities in a system of $L$ spins saturate at a value $P_{sat}(β, L) = (β/L)^αf(β)$, where $α$ remains constant for all $β\neq 0$ supporting the existence of the dynamic phase transition at $β=0$. The scaling function $f(β)$ shows a crossover behaviour with $f(β) = \rm{constant}$ for $β<<1$ and $f(β) \propto β^{-α}$ for $β>>1$.

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